Determine which of the rational functions given below has the following feature(s).
-There is a "hole" in its graph at $x = 5$
A) $f ( x ) = \frac { x + 9 } { x - 5 }$
B) $f ( x ) = \frac { 5 x - 1 } { x + 9 }$
C) $f ( x ) = \frac { ( x - 5 ) ( x + 9 ) } { ( x + 5 ) ( x - 5 ) }$
D) $f ( x ) = \frac { x + 5 } { ( x + 9 ) ( x + 5 ) }$

Question

Quizplus · Accepted Answer

A "hole" in the graph of a rational function occurs at a value of $x$ where both the numerator and denominator have a common factor that can be canceled out. In option C, the factor $x - 5$ is present in both the numerator and denominator, which means there will be a hole in the graph at $x = 5$ after this factor is canceled.

Determine Which of the Rational Functions Given Below Has the Following